228 BELL SYSTEM TECHNICAL JOURNAL 



using a crystal and coil in one arm of the lattice and electrical elements 

 in the other. Band-pass, band elimination, high and low-pass, and 

 all-pass filters result. Only the simplest combinations of resonant 

 frequencies giving the highest amount of attenuation are shown. As 

 in filters 4 and 6 of Fig. 2, some of the anti-resonances and resonances 

 of the two arms may be made to coincide giving filters with less 

 attenuation but more flexibility in the impedance characteristics. 

 Condensers can be incorporated in parallel or series with the crystals 

 without affecting the type of characteristic obtained. This procedure 

 is useful in controlling the widths of the pass or attenuation bands 

 and in controlUng the position of the peak values. In a number of 

 the filters of Figs. 3 and 4, the equivalent circuit of the crystal occurs 

 in the electrical circuit in the lattice arms. In these filters, crystals 

 can also be used in the lattice arms. Filters 1 and 5 of Fig. 3 and 

 filters 2 and 6 of Fig. 4 are band-pass filters which have been discussed 

 in detail in former papers.^- ^ 



Crystals may also be used in more complicated electrical circuits, 

 for example with transformers as shown in Fig. 5. This figure shows 

 high, low, band-pass, band elimination and all-pass filters which can 

 be constructed by employmg transformers and crystals in each arm. 

 More complicated structures still using single crystals can also be 

 constructed but they tend to be of less importance since the dissipation 

 introduced by the electrical elements neutralizes any benefit of using 

 crystals. 



It is possible, however, to use more crystals than one in one arm of 

 a lattice and obtain filters having higher insertion losses outside the 

 band without introducing more loss due to the electrical elements in 

 the band. Figure 6 shows a number of such combinations with and 

 without coils. The result of adding an additional crystal in one arm 

 of a lattice is to add another elementary section of the type discussed 

 in Appendix I. An example ^ of the characteristic obtainable with a 

 band-pass filter with two crystals in each arm is shown on Fig. 7. 



All of the filters discussed above were assumed to be constructed 

 from dissipationless elements. When coils are used, however, a 

 certain amount of resistance is associated with them which may alter 

 the characteristics obtainable. As has been pointed out previously,^ 

 if the dissipation associated with the coils can be brought out to the 

 ends of the arm either in series or parallel with the complete arm the 

 effect of these resistances will be to add a constant loss independent of 



^' ^ Loc. cit. 



* This filter was constructed and tested by Mr. H. J. McSkimin. 



* Loc. cit. 



